Anomalies at finite density and chiral fermions

TL;DR

This paper investigates the robustness of the chiral anomaly at finite chemical potential using perturbative and non-perturbative methods, and proposes a new approach for incorporating chemical potential in lattice fermions.

Contribution

It demonstrates the invariance of the chiral anomaly at nonzero chemical potential and introduces a simpler method for including chemical potential in lattice fermion formulations.

Findings

Chiral anomaly remains unaffected by finite chemical potential.

A new simpler method for incorporating chemical potential in lattice fermions.

Comparison with existing Bloch-Wettig approach.

Abstract

Using perturbation theory in the Euclidean (imaginary time) formalism as well as the non-perturbative Fujikawa method, we verify that the chiral anomaly equation remains unaffected in the presence of nonzero chemical potential, $\mu$. We extend our considerations to fermions with exact chiral symmetry on the lattice and discuss the consequences for the recent Bloch-Wettig proposal for the Dirac operator at finite chemical potential. We propose a new simpler method of incorporating $\mu$ and compare it with the Bloch-Wettig idea.